diff --git a/monitor/fsstate.go b/monitor/fsstate.go
index 42299d1..8ad7851 100644
--- a/monitor/fsstate.go
+++ b/monitor/fsstate.go
@@ -86,7 +86,7 @@ func (s *FilesystemState) StoreLogState(ctx context.Context, logID LogID, state
 	return writeJSONFile(filePath, state, 0666)
 }
 
-func (s *FilesystemState) StoreSTH(ctx context.Context, logID LogID, sth *cttypes.SignedTreeHead) error {
+func (s *FilesystemState) StoreSTH(ctx context.Context, logID LogID, sth *cttypes.SignedTreeHead) (*StoredSTH, error) {
 	sthsDirPath := filepath.Join(s.logStateDir(logID), "unverified_sths")
 	return storeSTHInDir(sthsDirPath, sth)
 }
diff --git a/monitor/monitor.go b/monitor/monitor.go
index 04abd0d..3af2d8f 100644
--- a/monitor/monitor.go
+++ b/monitor/monitor.go
@@ -29,7 +29,8 @@ import (
 )
 
 const (
-	getSTHInterval = 5 * time.Minute
+	getSTHInterval    = 5 * time.Minute
+	maxPartialTileAge = 5 * time.Minute
 )
 
 func downloadJobSize(ctlog *loglist.Log) uint64 {
@@ -270,12 +271,13 @@ retry:
 
 	// generateBatchesWorker ==> downloadWorker ==> processWorker ==> saveStateWorker
 
+	sths := make(chan *cttypes.SignedTreeHead, 1)
 	batches := make(chan *batch, downloadWorkers(ctlog))
 	processedBatches := sequencer.New[batch](0, uint64(downloadWorkers(ctlog))*10)
 
 	group, gctx := errgroup.WithContext(ctx)
-	group.Go(func() error { return getSTHWorker(gctx, config, ctlog, client) })
-	group.Go(func() error { return generateBatchesWorker(gctx, config, ctlog, position, batches) })
+	group.Go(func() error { return getSTHWorker(gctx, config, ctlog, client, sths) })
+	group.Go(func() error { return generateBatchesWorker(gctx, config, ctlog, position, sths, batches) })
 	for range downloadWorkers(ctlog) {
 		downloadedBatches := make(chan *batch, 1)
 		group.Go(func() error { return downloadWorker(gctx, config, ctlog, client, batches, downloadedBatches) })
@@ -300,47 +302,18 @@ retry:
 	return err
 }
 
-func getSTHWorker(ctx context.Context, config *Config, ctlog *loglist.Log, client ctclient.Log) error {
-	for ctx.Err() == nil {
+func getSTHWorker(ctx context.Context, config *Config, ctlog *loglist.Log, client ctclient.Log, sthsOut chan<- *cttypes.SignedTreeHead) error {
+	ticker := time.NewTicker(getSTHInterval)
+	defer ticker.Stop()
+	for {
 		sth, _, err := client.GetSTH(ctx)
 		if err != nil {
 			return err
 		}
-		if err := config.State.StoreSTH(ctx, ctlog.LogID, sth); err != nil {
-			return fmt.Errorf("error storing STH: %w", err)
-		}
-		if err := sleep(ctx, getSTHInterval); err != nil {
-			return err
-		}
-	}
-	return ctx.Err()
-}
-
-type batch struct {
-	number     uint64
-	begin, end uint64
-	sths       []*StoredSTH     // STHs with sizes in range [begin,end], sorted by TreeSize
-	entries    []ctclient.Entry // in range [begin,end)
-}
-
-func generateBatchesWorker(ctx context.Context, config *Config, ctlog *loglist.Log, position uint64, batches chan<- *batch) error {
-	ticker := time.NewTicker(15 * time.Second)
-	var number uint64
-	for ctx.Err() == nil {
-		sths, err := config.State.LoadSTHs(ctx, ctlog.LogID)
-		if err != nil {
-			return fmt.Errorf("error loading STHs: %w", err)
-		}
-		for len(sths) > 0 && sths[0].TreeSize < position {
-			// TODO-4: audit sths[0] against log's verified STH
-			if err := config.State.RemoveSTH(ctx, ctlog.LogID, &sths[0].SignedTreeHead); err != nil {
-				return fmt.Errorf("error removing STH: %w", err)
-			}
-			sths = sths[1:]
-		}
-		position, number, err = generateBatches(ctx, ctlog, position, number, sths, batches)
-		if err != nil {
-			return err
+		select {
+		case <-ctx.Done():
+			return ctx.Err()
+		case sthsOut <- sth:
 		}
 		select {
 		case <-ctx.Done():
@@ -348,68 +321,125 @@ func generateBatchesWorker(ctx context.Context, config *Config, ctlog *loglist.L
 		case <-ticker.C:
 		}
 	}
-	return ctx.Err()
 }
 
-// return the time at which the right-most tile indicated by sths was discovered
-func tileDiscoveryTime(sths []*StoredSTH) time.Time {
-	largestSTH, sths := sths[len(sths)-1], sths[:len(sths)-1]
-	tileNumber := largestSTH.TreeSize / ctclient.StaticTileWidth
-	storedAt := largestSTH.StoredAt
-	for _, sth := range slices.Backward(sths) {
-		if sth.TreeSize/ctclient.StaticTileWidth != tileNumber {
+type batch struct {
+	number       uint64
+	begin, end   uint64
+	discoveredAt time.Time        // time at which we became aware of the log having entries in range [begin,end)
+	sths         []*StoredSTH     // STHs with sizes in range [begin,end], sorted by TreeSize
+	entries      []ctclient.Entry // in range [begin,end)
+}
+
+// create a batch starting from begin, based on sths (which must be non-empty, sorted by TreeSize, and contain only STHs with TreeSize >= begin)
+func newBatch(number uint64, begin uint64, sths []*StoredSTH, downloadJobSize uint64) *batch {
+	batch := &batch{
+		number:       number,
+		begin:        begin,
+		discoveredAt: sths[0].StoredAt,
+	}
+	maxEnd := (begin/downloadJobSize + 1) * downloadJobSize
+	for _, sth := range sths {
+		if sth.StoredAt.Before(batch.discoveredAt) {
+			batch.discoveredAt = sth.StoredAt
+		}
+		if sth.TreeSize <= maxEnd {
+			batch.end = sth.TreeSize
+			batch.sths = append(batch.sths, sth)
+		} else {
+			batch.end = maxEnd
 			break
 		}
-		if sth.StoredAt.Before(storedAt) {
-			storedAt = sth.StoredAt
-		}
 	}
-	return storedAt
+	return batch
 }
 
-func generateBatches(ctx context.Context, ctlog *loglist.Log, position uint64, number uint64, sths []*StoredSTH, batches chan<- *batch) (uint64, uint64, error) {
+func appendSTH(sths []*StoredSTH, sth *StoredSTH) []*StoredSTH {
+	i := len(sths)
+	for i > 0 {
+		if sths[i-1].TreeSize == sth.TreeSize && sths[i-1].RootHash == sth.RootHash {
+			return sths
+		}
+		if sths[i-1].TreeSize < sth.TreeSize {
+			break
+		}
+		i--
+	}
+	return slices.Insert(sths, i, sth)
+}
+
+func generateBatchesWorker(ctx context.Context, config *Config, ctlog *loglist.Log, position uint64, sthsIn <-chan *cttypes.SignedTreeHead, batchesOut chan<- *batch) error {
 	downloadJobSize := downloadJobSize(ctlog)
-	if len(sths) == 0 {
-		return position, number, nil
+
+	// sths is sorted by TreeSize and contains only STHs with TreeSize >= position
+	sths, err := config.State.LoadSTHs(ctx, ctlog.LogID)
+	if err != nil {
+		return fmt.Errorf("error loading STHs: %w", err)
 	}
-	largestSTH := sths[len(sths)-1]
-	treeSize := largestSTH.TreeSize
-	if ctlog.IsStaticCTAPI() && time.Since(tileDiscoveryTime(sths)) < 5*time.Minute {
-		// Round down to the tile boundary to avoid downloading a partial tile that was recently discovered
-		// In a future invocation of this function, either enough time will have passed that this code path will be skipped, or the log will have grown and treeSize will be rounded to a larger tile boundary
-		treeSize -= treeSize % ctclient.StaticTileWidth
-		if treeSize < position {
-			// This can arise with a brand new log when config.StartAtEnd is true
-			return position, number, nil
+	for len(sths) > 0 && sths[0].TreeSize < position {
+		// TODO-4: audit sths[0] against log's verified STH
+		if err := config.State.RemoveSTH(ctx, ctlog.LogID, &sths[0].SignedTreeHead); err != nil {
+			return fmt.Errorf("error removing STH: %w", err)
 		}
+		sths = sths[1:]
 	}
+	handleSTH := func(sth *cttypes.SignedTreeHead) error {
+		if sth.TreeSize < position {
+			// TODO-4: audit against log's verified STH
+		} else {
+			storedSTH, err := config.State.StoreSTH(ctx, ctlog.LogID, sth)
+			if err != nil {
+				return fmt.Errorf("error storing STH: %w", err)
+			}
+			sths = appendSTH(sths, storedSTH)
+		}
+		return nil
+	}
+
+	var number uint64
 	for {
-		batch := &batch{
-			number: number,
-			begin:  position,
-			end:    min(treeSize, (position/downloadJobSize+1)*downloadJobSize),
+		for len(sths) == 0 {
+			select {
+			case <-ctx.Done():
+				return ctx.Err()
+			case sth := <-sthsIn:
+				if err := handleSTH(sth); err != nil {
+					return err
+				}
+			}
 		}
-		for len(sths) > 0 && sths[0].TreeSize <= batch.end {
-			batch.sths = append(batch.sths, sths[0])
-			sths = sths[1:]
+
+		batch := newBatch(number, position, sths, downloadJobSize)
+
+		if ctlog.IsStaticCTAPI() && batch.end%downloadJobSize != 0 {
+			// Wait to download this partial tile until it's old enough
+			if age := time.Since(batch.discoveredAt); age < maxPartialTileAge {
+				select {
+				case <-ctx.Done():
+					return ctx.Err()
+				case <-time.After(maxPartialTileAge - age):
+				case sth := <-sthsIn:
+					if err := handleSTH(sth); err != nil {
+						return err
+					}
+					continue
+				}
+			}
 		}
+
 		select {
 		case <-ctx.Done():
-			return position, number, ctx.Err()
-		default:
+			return ctx.Err()
+		case sth := <-sthsIn:
+			if err := handleSTH(sth); err != nil {
+				return err
+			}
+		case batchesOut <- batch:
+			number = batch.number + 1
+			position = batch.end
+			sths = sths[len(batch.sths):]
 		}
-		select {
-		case <-ctx.Done():
-			return position, number, ctx.Err()
-		case batches <- batch:
-		}
-		number++
-		if position == batch.end {
-			break
-		}
-		position = batch.end
 	}
-	return position, number, nil
 }
 
 func downloadWorker(ctx context.Context, config *Config, ctlog *loglist.Log, client ctclient.Log, batchesIn <-chan *batch, batchesOut chan<- *batch) error {
diff --git a/monitor/state.go b/monitor/state.go
index be2da47..bc1afed 100644
--- a/monitor/state.go
+++ b/monitor/state.go
@@ -54,7 +54,7 @@ type StateProvider interface {
 
 	// Store STH for retrieval by LoadSTHs.  If an STH with the same
 	// timestamp and root hash is already stored, this STH can be ignored.
-	StoreSTH(context.Context, LogID, *cttypes.SignedTreeHead) error
+	StoreSTH(context.Context, LogID, *cttypes.SignedTreeHead) (*StoredSTH, error)
 
 	// Load all STHs for this log previously stored with StoreSTH.
 	// The returned slice must be sorted by tree size.
diff --git a/monitor/sthdir.go b/monitor/sthdir.go
index f327a16..20c9aed 100644
--- a/monitor/sthdir.go
+++ b/monitor/sthdir.go
@@ -83,14 +83,26 @@ func readSTHFile(filePath string) (*StoredSTH, error) {
 	return sth, nil
 }
 
-func storeSTHInDir(dirPath string, sth *cttypes.SignedTreeHead) error {
+func storeSTHInDir(dirPath string, sth *cttypes.SignedTreeHead) (*StoredSTH, error) {
 	filePath := filepath.Join(dirPath, sthFilename(sth))
-	if fileExists(filePath) {
-		// If the file already exists, we don't want its mtime to change
-		// because StoredSTH.StoredAt needs to be the time the STH was *first* stored.
-		return nil
+
+	if info, err := os.Lstat(filePath); err == nil {
+		return &StoredSTH{
+			SignedTreeHead: *sth,
+			StoredAt:       info.ModTime(),
+		}, nil
+	} else if !errors.Is(err, fs.ErrNotExist) {
+		return nil, err
 	}
-	return writeJSONFile(filePath, sth, 0666)
+
+	if err := writeJSONFile(filePath, sth, 0666); err != nil {
+		return nil, err
+	}
+
+	return &StoredSTH{
+		SignedTreeHead: *sth,
+		StoredAt:       time.Now(), // not the exact modtime of the file, but close enough for our purposes
+	}, nil
 }
 
 func removeSTHFromDir(dirPath string, sth *cttypes.SignedTreeHead) error {